Aid effectiveness on GrowthA meta study

Hristos Doucouliagos and Martin Paldam

Working Paper No. 2005-13

DEPARTMENT OF ECONOMICS

Working Paper

ISSN 1396-2426

UNIVERSITY OF AARHUS C DENMARK

INSTITUT FOR ØKONOMIAFDELING FOR NATIONALØKONOMI - AARHUS UNIVERSITET - BYGNING 322

8000 AARHUS C - F 89 42 11 33 - TELEFAX 86 13 63 34

WORKING PAPER

Aid effectiveness on GrowthA meta study

Hristos Doucouliagos and Martin Paldam

Working Paper No. 2005-13

DEPARTMENT OF ECONOMICSSCHOOL OF ECONOMICS AND MANAGEMENT - UNIVERSITY OF AARHUS - BUILDING 322

8000 AARHUS C - DENMARK F +45 89 42 11 33 - TELEFAX +45 86 13 63 34

20/7-2005

Aid effectiveness on growth A meta study

Hristos Doucouliagos Department of Economics

Deakin University

Melbourne

Australia

and Martin Paldam Department of Economics

University of Aarhus

Aarhus

Denmark

Abstract:

The AEL (aid effectiveness literature) is econometric studies of the macroeconomic effects of

development aid. It contains about 100 papers of which 68 are reduced form estimates of the

effect of aid on growth in the recipient country. The raw data show that growth is

unconnected to aid, but the AEL has put so much structure on the data that all results possible

have emerged. The present meta study considers both the best-set of the 68 papers and the

all-set of 543 regressions published. Both sets have a positive average aid-growth elasticity,

but it is small and insignificant: The AEL has not established that aid works. Using meta-

regression analysis it is shown that about 20 factors influence the results. Much of the

variation between studies is an artifact and can be attributed to publication outlet, institu-

tional affiliation, and specification differences. However, some of the difference between

studies is real. In particular, the aid-growth association is stronger for Asian countries, and

the aid-growth association is shown to have been weaker in the 1970s.

JEL: B2, F35, O35

Keywords: Aid effectiveness, meta study, economic growth

Acknowledgement: Our cooperation was supported by the Aarhus University Research Foundation. Pia Wich-

mann Christensen has been a very competent research assistant. Tryggvi Thor Herbertsson, Peter Sandholt

Jensen are thanked for discussions inspiring this paper.

1. Introduction

Development aid is an important industry. At present the annual flow of transfers amounts to

more than US$60 billion. Many doubt the effectiveness of this flow on the welfare of recei-

ving nations. It is a sad fact that the basic model where growth is explained by aid on cross-

country or panel data shows that absolute aid effectiveness is rejected. This has led policy

makers to express concerns about the effectiveness of aid, while researchers have generated a

large and controversial literature trying to prove conditional aid effectiveness, where effecti-

veness is analyzed after the relation is controlled for country heterogeneity. However,

different authors have used different controls, and this has produced a wide range of results

which do not seem to converge.

The subject of the present paper, and two parallel ones, is thus the AEL, Aid Effective-

ness Literature. It analyzes the impact of aid empirically on macro economic data. A thorough

search of the literature gave a total of 97 AEL studies1 – they are listed in Appendix 2. Even

though there are almost 100 studies, the aid effectiveness controversy continues. Recently

most studies have found that aid does work under certain conditions, but may even be harmful

under other conditions. However, Hansen and Tarp (2000) claimed that (almost) all aid

works.

Accordingly, the aim of this paper is to use meta-analysis to synthesize the evidence.

Has the AEL established that aid has an impact on economic growth? And, if it has, how large

is it? Further, we use meta-regression analysis to investigate the source of heterogeneity/va-

riation in the available results. Till now the reviews of the AEL have been qualitative and

confined to only a portion of the available evidence, either because they are old as White

(1992) or Jepma (1995) or partial as Tsikaka (1998) or Hansen and Tarp (2000). Ours is the

first qualitative assessment of the entire body of evidence.

This paper is structured as follows: Section 2 defines and classifies the AEL and explo-

res some of the puzzles in the literature, while section 3 discusses the theory of the aid-growth

association. The data used for the meta-analysis are discussed in section 4. The heart of the

paper is sections 5 and 6, where the evidence is used to answer our key questions – is there an

aid-growth effect, and what explains the differences in results? The paper is concluded with a

number of suggestions for future research in section 7. Appendix 1 presents a short introduce-

tion to the techniques of meta-analysis, while Appendix 2 lists the AEL.

1. Extensive searches of Econlit, Proquest, Web of Science and Google were undertaken, from which we could track citations backward. Paper available after 1st of January 2005 are not included.

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2. The AEL and some aid-growth puzzles

The AEL asks if development aid is effective in generating development. The basic measure

for development is the economic growth rate. Consequently the AEL tries to answer the

question by estimating the effect, μ, of aid, h, on growth, g, using macro cross-country or

panel data, or time series data on individual countries. The 97 studies of the AEL use three

families of models characterized by their causal structure, as shown in figure 1. About half of

the studies contain estimates of models of more than one type. With the resulting overlapping

we have reached the following amounts of studies:

Figure 1. The causal structure in the three families of AEL models

A: 43 papers contain accumulation estimates of the impact of aid on savings or investment.

They are marked as type (s) and (i) in Appendix 2. These models are covered in Doucouliagos

and Paldam (2005a), which shows that aid has an unclear effect on accumulation.

B: 68 papers contain a total of 543 direct estimates, using reduced form models of the

effect of aid on growth. They are marked as type (g) in Appendix 2. They are the data of the

present meta-analysis.

C: 31 papers contain conditional estimates, where the effect of aid on growth depends

upon a third factor z, so that if z is favorable, the result is growth, and vice versa if z is unfa-

vorable. These studies are marked as type (c) in Appendix 2. They are covered in Doucou-

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liagos and Paldam (2005b). Till now 10 such z’s have been proposed, but none have survived

independent replications.

The AEL has been fuelled by the fact that the evidence is weak and contradictory. Notably

three pieces of evidence do not mesh:

(P1) Contrasting country stories: South Korea received substantial aid for a decade just

before its take off-into high growth. Tanzania has been a main recipient for 40 years, and has

had little growth. Considerable aid for 30 years to Zambia goes together with an unusually

poor economic performance.2

(P2) Micro-macro result: Studies summarizing project evaluations typically find that

about half of all projects succeed while the other half fails, but hardly any harms develop-

ment. Thus, by aggregation the micro evidence should show that aid increases growth.3

(P3) The zero correlation observation: The raw data for economic growth and the share

of development aid have no correlation – there is no absolute aid effectiveness as already

mentioned.4 It is puzzling indeed that the raw data show no relation between aid and growth.

(P3) contrasts with (P2). Since Mosely (1986), the contrast has been known as the micro-

macro paradox.

The zero-correlation-observation (P3) has an important implication: Any conclusion

that μ is non-zero, based on these data, must be due to the imposition of structure on the data.

Researchers have done this in four ways: (S1) Limit the data to a particular subset; (S2) aid is

only one factor of growth, so a control set, xj, of j other variables is often included in the aid-

growth relation; (S3) the (h,g)-relation is likely to have various biases, so researchers have

looked for the right estimator; and (S4) aid effectiveness may depend on something, so a con-

ditioning factor, z, has been entered in the relation – see the C group of studies above. Conse-

quently, many possibilities exist for applying structure to the data. This has allowed

researchers to reach all four possible answers to the AEL question. Namely, the effect of aid

on growth is: positive, insignificant, negative, or (in the studies of family C) it depends on

another variable, z, see here table 3 below.

2. Many country studies of the aid-growth connection exist, see e.g., White (1998). Below we only include country studies that contain econometric estimates. 3. The micro-macro result appears to be uncontroversial, see e.g. Cassen (1986, 1994) and IBRD-OED (annual). 4. The raw data for the AEL analysis are (h,g)-pairs averaged over, e.g. 4 years. The standard source, WDI, gives a total of 1008 such (h,g)-pairs (2005). Simple descriptive regressions between these data show no connection, see Doucouliagos and Paldam (2005c) and Herbertsson and Paldam (2005). This applies to cross-country reg-ressions and to panel regressions with and without controls for fixed effects and GDP-levels.

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The purpose of our study is to analyze the pattern in the answers. Why do some authors

find a positive effect, others no effect and still others a negative effect? Is the heterogeneity in

the estimates an artifact of the way studies are conducted (e.g. specification, estimation and

data differences), or does it reflect a real phenomenon associated with the existence of a

distribution of aid-growth effects?

The question lies at the heart of controversy over the impact of foreign aid. If differ-

rences in results are created by the application of structure to the data, then the information

available to taxpayers and policy makers is distorted, and we need to quantify the impact of

specification differences on aid-growth effects. If the variation in results is due to an underly-

ing distribution, so that aid increases growth in certain circumstances and decreases it in

others, then it is vital to identify the conditions and realign aid to take advantage of them.5

A look at the raw data permits us to make another point: From a statistical point of view

these data are ideal for AEL research: The (h,g)-data come in adequate numbers. The average

aid share is 7.4%. This is substantial relative to other variables that are found to effect growth,

i.e., it is about half the share of net investments, and larger than either the share of the

education budget or the share of the health budget in most LDCs. Furthermore, the standard

deviation of the aid share is 9.4, so aid data have considerable variation.

3. The models of the B family of the AEL

The basic modeling set-up is as listed in Table 1. Note that when the first papers were made in

the late 1960s few aid data were available, so panel estimation was impossible, but it was not

developed as an econometric technique, anyhow. Instead the older papers spent a lot of space

in the papers discussing politics/policy and economic theory.

Several of the early papers were rather explicit politically, with some researchers

belonging to the new left – notably Griffin (1970) and Weisskopf (1972) – while others were

explicitly libertarian – notably Friedman (1958) and Bauer (1971). Interestingly authors from

both schools believed that aid could easily become harmful to the recipient countries, though

for different reasons. Certainly excessive aid may distort the economy of a country and create

a low growth economy. Several studies of such extreme cases exist see e.g. Paldam (1997).

Economic theory enters as a frame of reference for the variables authors choose for controls 5. A parallel body of literature deals with the reverse causality. It explains aid flows (see Alesina and Dollar (2000). It does not point to growth in the recipient country as an important causal factor for giving aid. Hence, while reverse causality may give a bias in the AEL-relation, we expect that the bias is small. This is confirmed in Doucouliagos and Paldam (2005c).

4

and conditioning. That choice also depends upon the availability of the data. We have found

more or less explicit references to four types of economic theory in the AEL. Of which the

two first are discussed further in Doucouliagos and Paldam (2005a).

Table 1. The studies included are based on models of the following type

Model (1) git = α +μhit + γj xjit + uit Variable μ effect of aid, estimated

git real growth rate α, γj coefficients to be estimated hit aid as share of GDP, GNI it index to countries and time

xitj vectors of j controls uit residuals Note: The time unit is normally 3-5 years to reduce variation.

Type 1: IS-LM macro theory. The AEL deals with the activity, ΔY, which is caused in the

longer run, by an amount H of aid entering a country. The early AEL spent some effort on

classifying effects. Two main problems were found: (1) Aid is fungible, so what aid actually

finances is often different from the marginal outcome. The AEL tries to bypass the fungibility

complication by using reduced form estimates between aid and “final outcome” variables. (2)

The short-run activity effect should be separated out from the longer-run capacity effect,

which is the key purpose of aid. The (IS, LM)-framework suggests that there is both an

activity and a capacity effect.

Type 2: Two-gap models. For the first 2 decades of aid, its macro economic rationale

was Harrod-Domar type models, which were made explicitly to dynamize the IS-LM model.

The policy implication was that the main constraint to development was the savings necessary

to finance investments. The original Harrod-Domar model is a closed private sector model, so

savings are constrained by domestic savings behavior. The introduction of a public sector

budget balance gives the first gap. When the model is opened, the balance of payment provi-

des a second gap,6 where savings can be provided as transfers from the DC world. This is the

approach in the accumulation family of models. This model disappeared from the theory of

economic growth during the 1960s, but lingered on in development economics due to its

operationality and the clear policy prescriptions it generated.

However, gradually the Harrod-Domar framework was replaced by the more flexible

neo-classical framework, even in development economics. Since the 1990s, the AEL has used

6. The best known model of this type was Chenery and Strout (1966). Chapter 2 in Easterly (2001) gives the sad story of the savings gap in development.

5

state of the arts growth theory. It implies a richer set of channels from aid to growth, and

propose that aid effectiveness is analyzed directly from aid to growth.

Type 3: Barro type growth regressions. Since the early 1990s the best known empirical

tool in modern growth theory has been the Barro type growth regression,7 and it is what most

of the recent part of AEL has in mind. The model is set up to study convergence, i.e., the

coefficient β, to the GDP level, log ,ity in the following relation:

(2) see table 1 for definitions of variables. log ,it it jit jit itg yα β= + + +γ x u

u

If we treat log yit as one of the controls (2) turns into model (1) from table 1. These regres-

sions have been run for many x-sets, time periods, country sets, and with different estimators:

As a pure cross-country with no t-index, as a panel regression with both indices, or as time-

series data with only the t-index. Also, biases have been removed by doing TSIV-estimates

using some of the controls in the first stage, or as GMM-estimates using lags systematically.

These equations are simple and easy to use, and they have some relation to the neoclas-

sical growth model as discussed in Barro and Sala-i-Martin (2004). However, the connection

is weak, in the sense that the model only suggests some of the controls, while others are deba-

table ad hoc variables. Also, the choice of variables is often based on data availability. A

large number of model variants are easy to propose and estimate, and it is impossible to tell

what the right specification is, though some specifications are easier to justify than others.

The one-equation estimate of μ may easily be biased. Some examples may suffice. The

standard Barro estimates have the share of public consumption, cit, as one of the variables in

the x-set. If c is singled out the model looks like this:

(3) it it it jit jit itg h cα μ ν= + + + +γ x

One of Barro’s results is that public consumption is harmful for growth, ν < 0.8 Imagine a

full crowding out of the capacity effect of aid, so that aid only increases c. Then surely (3)

biases the estimate of μ upwards. However, Barro’s control set also includes variables for

education and health, which are assisted by aid and have a positive effect on growth. If they

are left in, it biases the estimate of μ downwards.

7. It is published in various versions since 1991. The newest is Barro and Sala-i-Martin (2004; cpt. 12). 8. That result is neatly reproduced in the AEL. When cit is included in the AEL relation it gets a negative coefficient, which is often significant. However, the negative coefficient to cit in the Barro equation is disputed.

6

Type 4: Political economy model. A new approach notes that aid is a new external rent

entering the economy. Here it may influence domestic political stability, and consequently

growth via the stability-growth channel: If political stability changes, the investment climate

improves, investment changes and so does growth. An extra rent can in principle have two

effects: It may turn some internal distributional fights from a negative sum game into a

positive sum game, and hence be politically stabilizing and increase growth.9 Alternatively, it

is a new contestable rent that increases distributional fights, and reduces political stability and

growth as resources are often found to do, see e.g. Collier and Hoeffler (2000). This gives two

possible outcomes and hence a subject for empirical analysis.

The theories referred to in the AEL are thus a well-known set of theories, which has

changed in line with the general development of economic theory. Before we turn to the

survey of papers, a few words should be added about the techniques used.

Estimators: All models can be estimated by a rapidly growing battery of estimators.

The choice appears to depend primarily on availability. When a new tool appears, it moves

the frontier of best practice outward. Consequently the new tool has to be applied for articles

to be accepted. However, only one example (Giles 1994) has been reported in any of the

papers in the AEL where the use of more advanced econometrics has changed the substantial

results (from just below to above significance).10 We test for the effect of estimation techni-

que below, and find that it does not appear to matter.

4. Two data sets for the meta study: The best-set and the all-set

The data we wish to submit to our analysis is the population of the AEL. A comprehensive

search revealed 97 studies, which explored the impact of foreign aid on savings, investment or

growth. Table 2 lists the number of studies and estimates that are used in our meta-analysis.

While in some models a positive impact of aid on investment does cause a positive impact on

growth, we prefer to separate the former studies from the latter. Accordingly, we separate

these studies into different categories as pictured in Figure 1.

In this paper we focus only on the foreign aid and economic growth literature of column

B of Table 2. Our measure of size of the effect is the partial correlation between foreign aid

and economic growth. While most studies provide enough information from which to calcu-

9. If distributional fights had no costs, they would, of course, be zero-sum games. 10. The AEL thus seems to support the critique of econometrics in chapter 6 of McCloskey (1998).

7

late the elasticity of growth with respect to foreign aid, many do not.11 Hence, we use partial

correlations as this enables us to include all available empirical studies.

Table 2. Statistics of the AEL

A: Accumulation B: Growth C: Conditional Proxy Sum Savings Investments Good Policy Medicine Others Papers, best-set 21 37 68 23 15 10 8 182 Regressions, all-set 61 122 543 162 85 23 29 1025 Sample size 1890 3872 11312 5523 4284 663 2264 29976 Note: The proxy studies are the ones where the empirics use aid-proxy data – such as capital inflows – to draw

conclusions regarding aid. This was often done in the early papers, where few aid data existed.

Table 2 shows that the AEL has published 1025 regressions, and the aggregated sample used

is 29,976 observations. The total number of annual observations for aid and growth available

is about 4,050, so the size of the effort made has led to massive data mining. We have

concentrated the discussion of data mining in Doucouliagos and Paldam (2005c). Appendix 1

explains how the statistics deals with this problem.

We derive two data sets. The best-set consists of 68 observations, one from each of the

68 papers, using the key regression from each paper. The all-set consists of 543 regressions

reported in the 68 papers, greatly increasing the data available for tests, but it gives some

interdependence between data points.

The papers are: Griffin and Enos (1970); Kellman (1971); Papanek (1973); Gupta

(1975); Stoneman (1975); Gulati (1976; 1978); Mosley (1980); Dowling and Hiemenz

(1983); Gupta and Islam (1983); Singh (1985); Landau (1986; 1990); Mosley et al. (1987;

1992); Levy (1988); Rana and Dowling (1988); Mahdavi (1990); Gyimah-Brempong (1992);

Islam (1992); Lensink (1993); Mbaku (1993); Snyder (1993); Boone (1994); Giles (1994);

Murty, Ukpolo and Mbatu (1994); Bowen (1995); Hadjimichael et al. (1995); Reichel (1995);

Most and van den Berg (1996); Amavilah (1998); Durbarry, Gemmell and Greenaway (1998);

Campbell (1999); Fayissa and El-Kaissy (1999); Svensson (1999); Burnside and Dollar

(2000; 2004); Hansen and Tarp (2000; 2001); Lensink and Morrisey (2000); Collier and Dehn

(2001); Dalgaard and Hansen (2001); Gounder (2001); Guillaumont and Chauvet (2001);

Hudson and Mosley (2001); Larson (2001); Lensink and White (2001); Lu and Ram (2001);

Teboul and Moustier (2001); Collier and Dollar (2002); Gomanee, Girma and Morrissey

(2002); Brumm (2003); Dayton-Johnson and Hoddinott (2003); Denkabe (2003); Easterly 11. These are typically studies that do not measure aid as the percentage of GDP.

8

(2003); Kosack (2003); Moreira (2003); Ovaska (2003); Ram (2003; 2004); Chauvet and

Guillaumont (2004); Collier and Hoeffler (2004); Dalgaard, Hansen and Tarp (2004);

Easterly, Levine and Roodman (2004); Economides et al. (2004); Jensen and Paldam (2004);

Roodman (2004); and Shukralla (2004);

Figure 2. Funnel plot: Partial correlations of aid and growth

Figure 2 is a funnel plot of the partial correlations, showing their association to the sample

size, for the all-set and best-set, respectively. It is obvious that the best-set is more extreme

than the all-set – researchers prefer regressions that show something. A majority of the esti-

mates are positive, but most are statically insignificant. The weighted average partial correla-

tion is +0.07 for the all-set and is +0.09 for the best-set, with sample size used as weights.12

Funnel plots should be symmetrical around the true population effect, if there is only one, and

12. Standard practice in meta-analysis requires that effect sizes (such as correlations) are weighted by the sample size of the study assuming that larger studies will, ceteris paribus, be more accurate (Hunter and Schmidt 2004).

9

the sampling error should be larger for the smaller studies so we expect that they are more

spread out than the larger studies. Both properties appear to be present.

Figure 3 is a time series graph of the empirical findings presenting the same partial cor-

relations as in Figure 2, but this time in chronological order. It is clear that although most

results are above zero, they fluctuate around the zero line, and they have a slight downward

time trend.13

Figure 3. Time series graph of aid-growth partial correlations

The downward trend in the 543 results of the AEL shown on figure 3 may have two explana-

tions: (E1) Aid has a declining effectiveness over time, or (E2) the increasing number of

observations makes data mining – for positive results – increasingly difficult. These possibili-

ties are further analyzed below. It will be demonstrated that (E2) is the better explanation.

4. Anatomy of failure: The ineffectiveness result

In this section we show that the conclusion that can be drawn from the entire extant literature

is that it has not proved that aid affects growth. However, there is evidence of heterogeneity,

13. The trend line drawn is +0.18538 –0.00027n, where n = 1, … 543. The t-ratio of the slope is -4.42.

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raising hope that aid may contribute to growth under certain circumstances. Appendix 1 gives

a brief introduction to the meta-analysis and the tests used.

4.1 Vote counting

Table 3 classifies the empirical results by sign and statistical significance. As explained in

Appendix 1, this is almost an extreme bounds analysis, but it is not a reliable way to summa-

rize the results of a literature. However, it offers a first overview of what the literature has

established. As suggested by figure 2, the best-set has relatively more significant results.

Almost half, 46%, of the 68 studies found a significantly positive effect, while 54% are either

not statistically significant or negative. Much the same pattern appeared in the 543 estimates

of the all-set. This can also be seen in Figure 4, which is a histogram of the 543 t-statistics

reported in the AEL. The average t-statistic is 1.05, the median is 1.15, and the weighted

average t-statistic is 1.22 (using sample size as weights).

Table 3. Meta extreme bounds analysis Group Positive Negative

Significant Insignificant Insignificant Significant 68 Studies 31 (46%) 22 (32%) 9 (13%) 6 (9%)

543 estimates 207 (38%) 198 (36%) 106 (20%) 32 (6%)

Figure 4. Histogram of t-statistics

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Table 4 gives the standard meta-analysis tests made to determine: (M1) Do the results of all

studies combined indicate the presence of a genuine effect among the two variables. This is

tested by the MST test and the MSTMRA test given in columns (1) to (4) of the table. The

desired outcome for a genuine effect is that that the coefficient to ln(df) should be

significantly positive. This is not the case. (M2) Does the literature suffer from polishing

effects, so that the results are too good in small samples? This is tested by the FAT-tests of

columns (5) and (6) of the table, where the desired outcome (for no polishing) is that the

constant is zero. The FAT tests show that results are polished in the AEL. This is the typical

finding in meta-analysis (Stanley 2005).

Table 4. Meta-significance and funnel asymmetry tests

(1) (2) (3) (4) (5) (6) MST MST MSTMRA MSTMRA FAT FAT

Appendix (3A) (3A) (7A) (7A) (5A) (5A) Variable All-set Best-set All-set Best-set All-set Best-set Constant 0.27 (1.14) 1.05 (1.20) -0.96 (-1.09) 1.00 (0.92) 1.71 (3.69)*** 3.78 (1.46) ln(df) -0.04 (-0.77) -0.17 (-0.97) 0.01 (0.03) -0.16 (-0.77) - - 1/SE - - - - -0.002 (-0.32) -0.006 (-0.17)Adjusted R2 0.00 0.01 0.11 0.08 0.00 0.00 F-statistic 0.76 3.52 1.96*** 1.62 0.10 0.03 N 543 68 418 63 540 65

Note: *, **, *** statistically significant at the 10%, 5% and 1% level, respectively. t-statistics in brackets.

5. Meta-regression analysis In the previous section it was shown that there is a positive, but statistically insignificant

association between development aid and economic growth. In this section we use meta-reg-

ression analysis to take a closer look at the variation in the empirical results and identify some

of the sources of these differences. Meta-regression analysis is gaining widespread appeal

among economists, and the AEL is fertile ground for its application. Recent examples include

Gorg and Strobl (2001), Doucouliagos and Laroche (2003) and Jarrell and Stanley (2004).

5.1 Variables

The variables used in our meta-regression analysis (MRA) are defined in table 6. We consider

six classes of explanatory variables:

12

Table 6. Definition of variables and their size and effect, when used alone

Variable BD means binary dummy that is 1 if condition fulfilled, otherwise 0 Mean SD Eff. ProbDependent The partial correlation of aid and economic growth 0.11 0.22 - - (C1) Publication Outlet WorkPap BD for unpublished paper 0.26 0.44 -0.05 0.003Cato BD for Cato Journal 0.03 0.16 0.08 0.04JDS BD for Journal of Development Studies 0.08 0.27 0.01 0.71JID BD for Journal of International Development 0.05 0.22 -0.01 0.80EDCC BD for Economic Development and Cultural Change 0.06 0.23 -0.16 0.00AER BD for American Economic Review 0.04 0.20 -0.11 0.00AE BD for Applied Economics 0.11 0.31 0.04 0.38 (C2) Author Details Danida BD for author(s) affiliated with the Danida group 0.09 0.29 0.01 0.50WorldBk BD for author(s) affiliated with the World Bank 0.09 0.29 -0.15 0.00Gender BD if at least one of the authors is female 0.12 0.33 0.03 0.39Expectations BD for author with realized expectations about aid-growth relation 0.10 0.30 -0.05 0.02Influence BD for authors acknowledging other authors in the AEL 0.22 0.42 0.03 0.15 (C3) Data Panel BD for use of panel data 0.67 0.47 -0.06 0.01NoCount Number of countries included in the sample 48 28 -0.09 0.02NoYears Number of years covered in the analysis 20 8 -0.01 0.00Africa BD for countries from Africa included 0.83 0.37 -0.13 0.00Asia BD if countries from Asia included 0.75 0.43 -0.02 0.49Latin BD if countries from Latin America included 0.76 0.43 -0.09 0.01Single BD if data from a single country 0.05 0.22 0.16 0.08Y1960s BD if data for the 1960s 0.21 0.40 0.02 0.53Y1970s BD if data for the 1970s 0.81 0.39 -0.11 0.00Y1980s BD if data for the 1980s 0.84 0.37 -0.10 0.00SubSam BD if data relate to a sub-sample of countries 0.28 0.45 0.03 0.18LowInc BD if data relate to a sub-sample of low income countries 0.09 0.28 -0.03 0.38EDA BD for use of EDA data 0.24 0.43 -0.10 0.00Outlier BD if outliers were removed from the sample 0.13 0.34 -0.05 0.00 (C4) Conditionality Nonlinear BD for aid squared added 0.18 0.38 0.03 0.03AidPolicy BD for aid interacted with policy 0.26 0.44 -0.10 0.00Institutions BD for other aid interacted terms (mainly institutions) 0.26 0.44 -0.21 0.00 (C5) Specification and Control Capital BD for control for domestic savings or investment 0.47 0.50 0.14 0.00FDI BD for control for foreign capital inflows (other than aid) 0.27 0.44 0.10 0.00GapModel BD for two-gap model 0.28 0.45 0.07 0.01Theory BD for paper developing a theory 0.30 0.46 -0.05 0.02Average Number of years involved in data averaging 6.7 5.4 0.01 0.58LagUsed BD for use of lagged value of aid 0.11 0.31 0.06 0.13Inflation BD for control for inflation 0.14 0.35 -0.03 0.05Instability BD for control for political instability 0.29 0.46 -0.08 0.00Fiscal BD for control for fiscal stance 0.12 0.32 0.00 0.96GovSize BD for control for size of government 0.12 0.32 0.05 0.01FinDev. BD for control for financial development 0.32 0.47 -0.04 0.03Ethno BD for control for ethnographic fractionalization 0.32 0.47 -0.09 0.00Region BD for regional dummies 0.36 0.48 -0.08 0.00HumCap BD for control for human capital 0.25 0.43 -0.02 0.42Open BD for control for trade openness 0.29 0.46 0.06 0.00PopSize BD for control for population size 0.29 0.46 0.06 0.01GdpLev BD for control for per capita income 0.63 0.48 -0.11 0.00Policies BD for control for policies 0.35 0.48 -0.10 0.00

(C6) Estimation OLS BD for use of OLS 0.68 0.47 0.04 0.002Gr&Aid BD for equations system with both a growth and an aid equation 0.04 0.20 0.07 0.00Gr&Savings BD equations system with both a growth and a savings equation 0.02 0.13 0.08 0.04

13

The two first are general priors of (C1) journals and (C2) authors. Such priors are explored by

8 publication outlet dummies and 6 author characteristics. The remaining 4 classes of variab-

les are (C3) 14 data characteristics, (C4) 18 variables for model formulation and controls,

(C5) are 4 variables for the inclusion of conditional variables, where aid is supplemented with

a second order aid term, and finally (C6) are 3 variables for estimation techniques.

Note that (at least) two of the variables are encompassing variables: DevJourn and

AidBus are thus encompassing several other more partial variables. We have calculated the

effect of each variable separately in the two right-hand columns, and the effects of groups of

variables and all (non-encompassing) variables are analyzed in tables 7a and 7b.

As regards (C2) we are influenced by our findings on the aid-conditionality literature,

which found that two prolific groups produced significantly different results: One was affili-

ated with the World Bank and the other with Danida (Danish Development Aid). The variable

influence tests whether “friends” acknowledged in the paper may influence results.

The 14 variables (C3) for data differences try to capture the differences in data used by

researchers. This includes controls for type of data (typically panel or cross-sectional), sample

size (countries and years), region (Africa, Asia, Latin America), time period covered, and

whether parts of samples are used (sub-sample, low income sample and removal of outliers).

Model specifications (C4) are made to influence results – we use 18 variables that capture

most of the differences in specifications, and are hence able to perform a meta-robustness

testing. Through these we are able to explore how robust the aid-growth effects are and can

quantify the effects of changing specification, as well as data differences etc.

5.2 Explaining the partial correlation between aid and economic growth

The MRA results are presented in Table 7a using OLS on the all-set. Several alternative spe-

cifications are given to explore the sensitivity of the results. Table 7b considers alternative

regression techniques on both the all-set and the best-set. In both tables the dependent

variable is the partial correlation between foreign aid and economic growth.

14

Table 7a. OLS Meta-Regression Analysis, all-set Variable (1) (2) (3) (4) (5)Constant 0.19 (11.81)*** 0.39 (6.45)*** 0.04 (0.69) 0.36 (2.65)*** 0.19 (6.50)***WorkPap -0.08 (-4.74)*** - - 0.03 (0.58) 0.03 (1.67)*Cato -0.11 (-2.62)*** - - -0.05 (-0.50) - JDS -0.05 (-1.96)* - - 0.01 (0.05) - JID -0.07 (-2.86)*** - - -0.09 (-1.58) -0.7 (-2.12)**EDCC -0.23 (-3.92)*** - - -0.62 (-3.60)*** -0.59 (-3.64)***AER -0.14 (-6.47)*** - - -0.01 (-0.15) - AE -0.04 (-0.73) - - -0.11 (-1.63) -0.15 (-2.48)**Danida - 0.06 (2.81)*** - 0.12 (2.25)** 0.13 (4.55)***WorldBk - -0.12 (-5.34)*** - 0.05 (0.83) 0.06 (1.74)*Gender - 0.01 (0.17) - 0.02 (0.19) - Expectations - 0.07 (2.79)*** - 0.02 (0.39) - Influence - 0.07 (4.03)*** - 0.10 (3.57)*** 0.12 (5.84)***Panel - 0.01 (0.31) - -0.01 (-0.21) - NoCount - -0.00 (-0.13) - -0.01 (-0.42) -0.001 (-2.41)**NoYears - 0.001 (0.02) - -0.01 (-0.14) - Africa - -0.07 (-1.52) - -0.03 (-0.65) - Asia - 0.10 (2.22)** - 0.10 (2.06)** 0.11 (3.04)***Latin - -0.14 (-2.94)*** - -0.06 (-1.19) - Single - 0.06 (0.52) - 0.20 (1.24) 0.27 (2.56)**Y1960s - -0.11 (-2.34)** - -0.04 (-0.73) - Y1970s - -0.10 (-2.38)** - -0.14 (-3.17)*** -0.13 (-3.91)***Y1980s - -0.12 (-2.22)** - -0.12 (-1.66) - SubSam - -0.01 (-0.28) - -0.03 (-0.96) - LowInc - 0.01 (0.01) - 0.02 (0.38) - EDA - -0.07 (-3.62)*** - -0.05 (-2.25)** -0.07 (-3.86)***Outlier - -0.03 (-1.79)* - -0.01 (-0.11) - Nonlinear 0.04 (2.93)*** - - -0.01 (0.61) - AidPolicy -0.07 (-5.07)*** - - 0.01 (0.56) - Institutions -0.21 (-7.06)*** - - -0.11 (-2.52)** -0.11 (-3.82)***Capital - - 0.13 (2.53)** 0.06 (1.26) - FDI - - 0.04 (1.05) 0.06 (1.36) 0.09 (3.49)***GapModel - - -0.08 (-1.83)* -0.05 (-0.63) - Theory - - 0.02 (0.75) -0.02 (-0.41) - Average - - 0.00 (0.56) 0.00 (0.08) - LagUsed - - 0.01 (0.30) 0.06 (1.18) - Inflation - - -0.05 (-1.83)* -0.07 (-1.77)* -0.05 (-2.47)**Instability - - -0.01 (-0.36) 0.10 (1.55) 0.13 (2.71)***Fiscal - - 0.06 (1.50) 0.05 (1.11) - GovSize - - 0.07 (2.82)*** 0.09 (2.39)** 0.09 (4.24)***FinDev - - 0.03 (1.21) 0.03 (0.96) 0.04 (2.31)**Ethno - - 0.00 (0.11) -0.11 (-2.03)** -0.16 (-3.48)***Region - - -0.04 (-2.15)** -0.02 (-0.87) - HumCap - - -0.10 (-3.52)*** -0.04 (-0.75) - Open - - 0.00 (0.10) -0.01 (-0.22) - PopSize - - 0.04 (1.59) -0.03 (-0.58) - GdpLev - - 0.00 (0.06) 0.04 (0.92) - Policies - - -0.03 (-1.24) -0.11 (-3.30)*** -0.12 (-5.51)***OLS - - 0.03 (1.93)* -0.01 (-0.47) - Gr&Aid - - 0.10 (2.68)*** -0.03 (-0.76) - Gr&Savings - - 0.02 (0.42) -0.02 (-0.48) - Adjusted R2 0.13 0.16 0.11 0.30 0.31Cor(ob, fit) 0.38 0.44 0.38 0.61 0.58N 543 474 539 474 487*, **, *** statistically significant at the 10%, 5% and 1% level, respectively. White heteroscedasticity-consistent standard errors and covariances used. t-statistics in brackets. Cor(ob, fit) is the correlation between observed and fitted partial correlations.

15

Table 7b. Sensitivity of Meta-Regression Analysis of table 7 (4) from 7a (6) (7) (8) OLS All-Set WLS All-Set OLS All-Set OLS Best-Set Variable General General Bootstrap General Specific Constant 0.36 (2.65)*** 0.49 (5.30)*** 0.36 (2.46)*** 0.15 (1.43) WorkPap 0.03 (0.58) -0.02 (-0.88) 0.03 (0.46) - Cato -0.05 (-0.50) -0.22 (-4.24)*** -0.05 (-0.50) - JDS 0.01 (0.05) -0.01 (-0.23) 0.01 (0.05) 0.23 (2.42)** JID -0.09 (-1.58) -0.07 (-2.15)** -0.09 (-1.43) - EDCC -0.62 (-3.60)*** -0.57 (-6.36)*** -0.62 (-3.56)*** -0.52 (-2.12)** AER -0.01 (-0.15) -0.02 (-0.36) -0.01 (-0.11) - AE -0.11 (-1.63) -0.12 (-2.14)** -0.11 (-1.56) - Danida 0.12 (2.25)** 0.09 (2.89)*** 0.12 (1.95)* - WorldBk 0.05 (0.83) -0.09 (-3.05)*** 0.05 (0.85) - Gender 0.02 (0.19) -0.08 (-2.54)** 0.02 (0.17) - Expectations 0.02 (0.39) 0.11 (3.73)*** 0.02 (0.36) - Influence 0.10 (3.57)*** 0.03 (1.82)* 0.10 (3.37)*** 0.09 (1.74)* Panel -0.01 (-0.21) 0.04 (0.89) -0.01 (-0.17) - NoCount -0.01 (-0.42) 0.001 (1.83)* -0.01 (-0.45) -0.004 (-3.04)*** NoYears -0.01 (-0.14) 0.001 (0.08) -0.01 (-0.21) - Africa -0.03 (-0.65) -0.10 (-2.34)** -0.03 (-0.55) - Asia 0.10 (2.06)** 0.04 (1.03) 0.10 (2.16)** 0.20 (2.18)** Latin -0.06 (-1.19) -0.02 (-0.56) -0.06 (-1.09) - Single 0.20 (1.24) 0.35 (2.95)*** 0.20 (1.15) - Y1960s -0.04 (-0.73) -0.03 (-1.29) -0.04 (-0.63) - Y1970s -0.14 (-3.17)*** -0.10 (-2.96)*** -0.14 (-3.31)*** -0.16 (-2.34)** Y1980s -0.12 (-1.66) -0.29 (-5.14)*** -0.12 (-1.62) - SubSam -0.03 (-0.96) -0.04 (-1.70) -0.03 (-0.96) - LowInc 0.02 (0.38) 0.02 (0.55) 0.02 (0.44) - EDA -0.05 (-2.25)** -0.04 (-2.26)** -0.05 (-1.76)* - Outlier -0.01 (-0.11) 0.00 (0.05 -0.01 (-0.10) - Nonlinear -0.01 (-0.61) 0.03 (1.65) -0.01 (-0.12) - AidPolicy 0.01 (0.56) 0.02 (0.85) 0.01 (0.50) - Institutions -0.11 (-2.52)** -0.05 (-2.04)** -0.11 (-2.94)*** - Capital 0.06 (1.26) 0.05 (1.43) 0.06 (1.11) 0.20 (4.02)*** FDI 0.06 (1.36) 0.08 (2.48)** 0.06 (1.13) - GapModel -0.05 (-0.63) -0.09 (-1.91)* -0.05 (-0.68) - Theory -0.02 (-0.41) -0.05 (-2.04)** -0.02 (-0.32) - Average 0.00 (0.08) -0.00 (-0.08) 0.00 (0.08) - LagUsed 0.06 (1.18) 0.08 (4.64)*** 0.06 (1.21) - Inflation -0.07 (-1.77)* -0.08 (-2.54)** -0.07 (-1.48) - Instability 0.10 (1.55) 0.01 (0.46) 0.10 (1.33) - Fiscal 0.05 (1.11) 0.01 (0.15) 0.05 (0.95) - GovSize 0.09 (2.39)** 0.06 (2.37)** 0.09 (2.20)** 0.19 (2.58)** FinDev 0.03 (0.96) 0.06 (3.44)*** 0.03 (0.92) - Ethno -0.11 (-2.03)** -0.01 (-0.22) -0.11 (-1.79)* - Region -0.02 (-0.87) -0.03 (-2.35)** -0.02 (-0.83) - HumCap -0.04 (-0.75) 0.05 (1.88)* -0.04 (-0.75) - Open -0.01 (-0.22) -0.03 (-1.37) -0.01 (-0.21) - PopSize -0.03 (-0.58) -0.02 (-1.03) -0.03 (-0.53) - GdpLev 0.04 (0.92) 0.01 (0.01) 0.04 (0.80) - Policies -0.11 (-3.30)*** -0.04 (-1.56) -0.11 (-2.48)** - OLS -0.01 (-0.47) -0.04 (-2.49)** -0.01 (-0.43) - Gr&Aid -0.03 (-0.76) -0.03 (-0.82) -0.03 (-0.61) - Gr&Savings -0.02 (-0.48) 0.01 (0.04) -0.02 (-0.34) - Adjusted R2 0.30 0.55 0.30 0.35 Cor(ob, fit) 0.61 0.54 0.61 0.66 N 474 474 427 63 Note: See table 7a. Column (4) is repeated for ease of cross-reference.

16

Tables 7a and b have a total of 8 columns, with different sets of variables and estimation

techniques. Not surprisingly, many of the variables are not statistically significant.14 However

several variables are significant as well as robust to specification of the MRA. Table 7b uses

WLS-regression in column (6). Normally, the inverse of the standard error variance is used as

weights (see Longhi et al. 2005). However, Hunter and Schmidt (2004) argue that sample size

is a better set of weights to use. The WLS results are broadly similar to the OLS results,

although there are some differences.15 Many of the observations are not strictly statistically

independent. Accordingly, column (7) reports the results of using the bootstrap to generate

standard errors. Once again, the results are broadly in line with the OLS results.16 Finally the

MRA was repeated for the best-set. The results after sequentially eliminating any statistically

insignificant variables are presented in column (8).17 There are much fewer degrees of

freedom, but the main results are the same as in the other columns.

(C1) Publication outlet: EDCC has a negative sign that is always statistically signifi-

cant, but it is mainly due to 3 papers written from a Marxist/Left-wing perspective. The

papers published in JDS tend to have positive results, but this journal may be seen as “belon-

ging” to the aid business. The two papers published in the Cato Journal have negative results,

as this journal has a libertarian orientation, which predicts negative effects of aid on growth.

AE and JID also have negative results, which are often significant. Note that these outlet

effects either reflect the editorial policy of the journals or the self-selection of authors.

(C2) Groups/influence: The most significant result here is that writers from the Danida

group consistently find results that are more pro-aid (with about 0.1 points) than others, while

the results for researchers from the World Bank deviate less from the other results.18

It is also important that the influence variable tends to be significant. Researchers tend

to confirm the results of those they are associated with. The influence variable has a robust

significant positive coefficient indicating that studies conducted by authors who receive com-

ments/assistance from other authors publishing in the same field tend to report higher partial

correlations. This does not mean, however, that these studies are biased. Indeed, they may be

better constructed ones.

14. Multicollinearity is often a problem with MRA, and note also that sample size changes as different variables are added/omitted. 15. We prefer the OLS results because the meta-regression WLS results can be influenced by outliers (see Hunter and Schmidt 2004). 16. The bootstrap used 1000 replications with replacement. 17. The WLS estimates for the best-set are broadly similar. Since there is no issue of statistical independence of the estimates in the best-set, there is no need to use the bootstrap to derive standard errors. 18. See however Doucouliagos and Paldam (2005b) on the results for the aid-policy interaction term.

17

(C3) Data. The number of countries included in a sample has a negative coefficient –

the larger the sample the weaker is the aid-growth effect. This result was found also by

Doucouliagos and Paldam (2005a) for the aid-conditionality literature. Ceteris paribus, we

would expect that if an aid growth association exists, it should be robust to sample size. This

confirms the results of the MST and FAT tests in table 4. The results from small samples are

polished, to make them too good – and that means too positive for aid. This confirms the

second hypothesis (E2) of the trend on figure 3.

The coefficient on NoCount captures the impact of sample size after controlling for

outliers. The negative coefficient on NoCount indicates that authors are able to select samples

to polish results (as did the FAT-test in table 4). There are often solid grounds for removing

outliers from samples. However, the Outlier variable was not statistically significant.

The three decade variables Y1960s to Y1980s show that the aid-growth association

reported was weaker in the 1970s, where many countries borrowed heavily on the commercial

market, and thus were less dependent on aid. Also, the 1970s were the period of the Oil Crisis

which generated rather strong economic fluctuations that were independent of aid.

The use of EDA as a measure of aid leads to lower aid-growth effects. The relation

between EDA and ODA data is: EDA = a ODA + ε, where a ≈ 0.42 and ε is small, as the

correlation between the two aid series is 0.83, where both are available. If decision makers

consider ε to be random, we expect the partial correlations to be exactly the same. However,

this is not likely, and the result then comes to depend upon the time horizon of the decision

makers. Imagine that the decision makers have a long time horizon. Then they recognize that

loans have to be paid back. Hence they react much stronger to EDA data than to the ODA

data. Thus the elasticities to the EDA data should be systematically larger. However, if the

decision makers are myopic then they react to ODA data and do not care about the size of the

gift element, which matters in the longer run only. Thus the elasticities to the ODA data

should be systematically larger. We actually find that the elasticities to the ODA data are

significantly higher and thus one more indication that decision makers are myopic.19

Regional differences in the aid-growth association are also detected. The inclusion of

Asian economies in a sample increases the association, which confirms that there is a

distribution of aid-growth associations – with aid having higher effects in some regions. This

19. This is the standard result in the literature on vote and popularity functions, see Nannestad and Paldam (1994). It is also the only really strong explanation for the phenomenon of debt crises, which seems to appear every 20-30 years in a surprising number of countries.

18

is an important factor that is a real phenomenon. The explanation for this variation is beyond

the scope of this paper. 20

(C5) Model formulation and controls. Here the results differ somewhat between tables

7a and 7b. While many of the variables are significant in some columns very few are robust

throughout. The most robust result for the (C4) variables is that controlling for the share of

government results in larger aid-growth effects, as predicted in section 3, where we argued

that it was an obvious misspecification to include the share of government, see the discussion

of equation (3). We note that it biases the results upward by about 0.1.21

(C6) Estimation techniques. As mentioned at the end of section 3 there is no apparent

difference in results according to the techniques used, once other study differences are

controlled for: cross-sectional, panel and time series data basically produce the same partial

correlation. Also, the choice of estimator leaves results unchanged. Using lagged values of aid

results in similar results as using current levels of aid.

The MRA explains about one third of the variation in results, with a reasonable degree

of correlation between the predicted partial correlations and the observed partial correlations,

which is good for this sort of analysis. This means also that the bulk of the variation is unex-

plained suggesting once again that there may be an undetected conditionality in the literature.

5.4 Meta-probit analysis

The MRA presented in Tables 7a and 7b explains some of the heterogeneity in reported

results. Doucouliagos and Paldam (2005a) estimate a meta-probit model to explore the

determinants of statistical significance. In this model, the dependent variable is a binary

variable assigned a value of 1 if the study found a positive and statistically significant effect

and 0 otherwise. We consider the same set of potential explanatory variables as in Tables 7

and 8, and report only those variables that were statistically significant. The four journals –

Cato, JID, EDCC and AE – all have negative coefficients, with marginal effects ranging from

0.12 to 0.28. Papers published in these journals are less likely to report statistically significant

results. Researchers associated with Danida are more likely to report statistically significant

results, while researchers associated with the World Bank are less likely to do so.

20. Note that we do not discuss the results for (C5), the conditionality variables. They are discussed in Doucouli-agos and Paldam (2005b). 21. This may explain why the Danida group gets coefficients that are 0.1 higher than the norm, as they do include the share of the government, and get the expected negative coefficient to that variable.

19

Table 9. Determinants of statistical significance Variable Coefficient z-Statistic Marginal Effect Constant -0.82 -5.25 Cato -3.17 -5.80 -0.28 JID -0.85 -3.08 -0.20 EDCC -1.47 -3.09 -0.26 AE -0.42 -2.08 -0.12 Danida 0.69 2.91 0.25 World Bank -1.31 -2.46 -0.26 Influence 0.59 3.35 0.21 Sub-Sample -0.68 -4.45 -0.20 Aid Square 1.30 6.58 0.47 Aid*Institutions -6.35 -38.10 -0.36 Capital 1.03 5.60 0.33 Inflation -0.43 -2.01 -0.12 Size of Government 1.40 5.07 0.51 McFadden R2 0.27 Sample Size 542

Note: The dependent variable is a binary variable reflecting whether the aid term of the study

has a positive and statistically significant impact on economic growth.

6. Summary and suggestions for future research

The AEL (aid effectiveness literature) has accumulated a large pool of evidence, and the

majority of the authors seem to agree that aid has a small positive effect on growth. The aim

of this paper was to apply the methods of meta-analyses to the entire literature to see if that

conclusion is justified. We used the population of 68 aid-growth studies as our data set. Our

conclusions are depressing: Taking all available evidence into consideration, we have to

conclude that the AEL has failed to prove that the effect of development aid on growth is

statistically significantly larger than zero.

We also investigated the variation in the available results. Some of this variation was

found to be a direct outcome of data and specification differences. In particular, we found that

journals, friends and institutional affiliation influences reported results. However, we found

also that some of the variation was real, e.g. including Asian economies in a sample increases

the reported effect of aid on growth. This literature has a larger variation than expected if it is

only random variation around one average. It actually suggests that there are several. This

lends support to the notion of conditionality: Perhaps aid does contribute to economic growth

under certain circumstances and not under other circumstances. The challenge for researchers

is to find what those circumstances are.

20

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22

Appendix 1: Introduction to meta techniques, especially to the tests used

Meta-analysis uses both descriptive statistics and significance tests, which are developed for the purpose. Note

especially that the significance tests have to take into account that all studies are based on a common pool of

available macro data that has been thoroughly mined.

Descriptive statistics

Two methods are in general use: Counts of coefficients with different signs and significance and calculations of

various averages.

A1 Vote counting

All existing reviews of the aid-growth literature have either explicitly or implicitly used vote counting. Vote

counting is similar to Extreme Bounds Analysis (EBA). In EBA, researchers use the same data set and explore

the impact of different control variables (see Barro and Sala-i-Martin 2004). The difference here is that rather

than the same sample being used with different specifications, we use different samples as well as different

specifications. This is effectively a meta-extreme bounds analysis (MEBA).

Counting the number of signs should not be given too much weight, as it does not provide a method for

research synthesis. Moreover, it ignores information provided by the confidence intervals. For example, Ram’s

(2004) estimate of the aid-growth elasticity has a 95% confidence interval of -0.37 to +0.33, while Economides

et al. (2004) estimate a confidence interval of +0.16 to +0.94. From Ram we conclude that there is a zero

elasticity and from Economides et al. that there is a positive elasticity. The two intervals do, however, intersect –

they both agree that it is possible that the elasticity may be +0.16 to +0.33. With meta-analysis we can combine

all studies and avoid the potential problems of sign counting.

A2 Average effects

The effect between two variables (holding other effects constant) established by a literature can be derived as a

weighted average of the associated estimates:

(1A) [ ] /i i iN Nε ε= ∑ ∑

where ε is the standardized effect (elasticity or partial correlation) from the ith study and N is the sample size.

A3 Confidence intervals

Confidence intervals in meta-analysis can be calculated in several ways. Hunter and Schmidt (2004) derive the

formula for the standard error in the mean correlation for a homogenous group of studies, as well as the standard

error in the mean correlation for a heterogeneous group of studies. Hedges and Oklin (1985) use a slightly

different procedure. We prefer to follow Adams et al. (1997) and use resampling techniques to construct boot-

strap confidence intervals, which are more conservative. The 95% confidence intervals of elasticities were

constructed using the bootstrap of 1000 iterations (with replacement) to generate the distribution of aid and aid-

23

growth interaction elasticities (see Efron and Tibshirani 1993). The lower and upper 2.5 % of the values of the

generated distribution are used to construct the 95 % confidence intervals.

Regression based tests

The data for the two following tests are a set of n estimates of the same effect, ε, with the associated tests

statistics (ti, si, di), where ti is the t-statistics; si, is the standard error; di is the degrees of freedom of the estimate.

All n estimates use variants of the same estimation equation and sub-samples of the same data. Both tests use the

population of observations and are robust to data mining.

A5 Meta-Significance Testing: The MST test (Stanley 2001; 2005)

The idea is that a connection between two variables, such as foreign aid and economic growth, should exhibit a

positive relationship between the natural logarithm of the absolute value of the t-statistic and the natural

logarithm (ln) of the degrees of freedom in the regression:

(3A) ln│ti│= α0 + α1 ln dfi + ui

As the sample size for the ith study rises, the precision of the coefficient estimate for the ith study rises also, i.e.,

standard errors fall and t-statistics rise. Stanley (2005) shows that the slope coefficient in equation (3A) offers

information on the existence of genuine empirical effects, publication bias, or both. If α1 < 0, the estimates are

contaminated by selection effects, because t-statistics fall as sample size rises. That is, studies with smaller

samples report larger t-statistics, indicating that it is easier to mine smaller samples in order to increase the

prospects of publication. If α1 > 0, there is a genuine association between aid policy interaction and economic

growth, since t-statistics rise as sample size increases. If 0 < α1 < 0.5, then there is a genuine association between

aid policy interaction and economic growth, as well as publication bias in the literature.

A6 Funnel-Asymmetry Testing: FAT tests (Egger et al. 1997; Stanley 2005)

Smaller samples have larger standard errors. If publication bias is absent from a literature, no association

between a study’s reported effect and its standard error should appear. However, if there is publication bias,

smaller studies will search for larger effects in order to compensate for their larger standard errors, which can be

done by modifying specifications, functional form, samples and even estimation technique.

(4A) ei = β0 + β1si + ui

where ei is the regression coefficient, and si is its standard error. Since the explanatory variable in equation (4A)

is the standard error, heteroscedasticity is likely to be a problem. Equation (4A) (from Stanley 2005) is corrected

for heteroscedasticity by dividing it by the associated standard error. This produces equation (5A):

(5A) ti = β1 + β0 (1/ si)+ vi

If publication bias is present, the constant, β1, in equation (5A) will be statistically significant.

24

A7 Meta-Regression Analysis

The impact of specification, data and methodological differences can be investigated by estimating a meta-

regression model (known as a MRA) of the following form:

(6A) roi = α + β1Ni + γ1Xi1 +…+ γkXik + δ1Ki1 +…+ δnKin + ui

where

roi is the observed partial correlation (or any other standardised effect) derived from the ith study,

α is the constant,

Ni is the sample size associated with the ith study,

Xij are dummy variable j representing characteristics associated with the ith study,

Kij are continuous variable j associated with the ith study, and

ui is the disturbance term, with usual Gaussian error properties (see Stanley and Jarrell 1998).

The regression coefficients quantify the impact of specification, data and methodological differences on reported

study effects (roi). Both the MST and FAT tests can be combined with the MRA. The MSTMRA tests used in

table 4 have the following form:

(7A) ln│ti│= α0 + α1 ln di + XXXX + ui

The test is the same as before: Is α1 < 0

25

Appendix 2: The AEL, aid effectiveness literature. This paper covers studies of type (g)

Only papers in English available till 1/1 2005 are included. Papers are classified in 7 types as regards the model

estimated: (s), (sp) and (i) are accumulation models, with savings, savings with aid proxies, and investment

relations respectively. (g) and (gc) are growth and conditional growth models.

No Type Author and publication details

1 sp Ahmed, N., 1971. A note on the Haavelmo hypothesis. Review of Economics and Statistics 53, 413-14

2 g Amavilah, V.H., 1998. German aid and trade versus Namibian GDP and labour productivity. Applied

Economics 30, 689-95

3 ig Boone, P., 1994. The impact of foreign aid on savings and growth. WP London School of Econ.

4 i Boone, P., 1996. Politics and the effectiveness of foreign aid. European Economic Review 40, 289-

329

5 sgc Bowen, J.L., 1995. Foreign aid and economic growth: An empirical analysis. Geographical Analysis

27, 249-61. Estimates also in Bowen, J.L., 1998. Foreign aid and economic growth: A

theoretical and empirical investigation. Ashgate, Aldershot, UK

6 s Bowles, P., 1987. Foreign aid and domestic savings in less developed countries: Some tests for

causality. World Development 15, 789-96

7 gc Brumm, H.J., 2003. Aid, policies and growth: Bauer was right. Cato Journal 23, 167-74

8 gc Burnside, C., Dollar, D., 2000. Aid, policies and growth. American Economic Review 90, 847-68

(Working paper available fro World bank since 1996)

9 gc Burnside, C., Dollar, D., 2004. Aid, policies and growth: Reply. American Economic Review 94, 781-

84 (reply to Easterly, Levine and Roodman, 2004)

10 sg Campbell, R., 1999. Foreign aid, domestic savings and economic growth: Some evidence from the

ECCB area. Savings and Development 23, 255-78

11 gc Chauvet, L., Guillaumont, P., 2004. Aid and growth revisited: Policy, economic vulnerability and

political instability. Pp 95-109 in Tungodden, B., Stern, N., Kolstad, I., eds, 2004. Toward

Pro-Poor Policies - Aid, Institutions and Globalization. World Bank/Oxford UP

12 gc Collier, P., Dehn, J., 2001. Aid, shocks, and growth. WP 2688 World Bank Policy Research

13 gc Collier, P., Dollar, D., 2002. Aid allocation and poverty reduction. European Economic Review 46,

1475-1500

16 i Collier, P., Dollar, D., 2004. Development effectiveness: What have we learnt? Economic Journal

114, 244-71

15 gc Collier, P., Hoeffler, A., 2004. Aid, policy and growth in post-conflict societies. European Economic

Review 48, 1125-45

16 gc Dalgaard, C.-J., Hansen, H., 2001. On aid, growth and good policies. Journal of Development Studies

37, 17-41

17 gc Dalgaard, C.-J., Hansen, H., Tarp, F., 2004. On the empirics of foreign aid and growth. Economic

Journal 114, 191-216

18 gc Dayton-Johnson, J., Hoddinott, J., 2003. Aid, policies and growth, redux. WP Dalhousie Univ.

26

19 gc Denkabe, P., 2004. Policy, aid and growth: A threshold hypothesis. Journal of African Finance and

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20 i Dollar, D., Easterly, W., 1999. The search for the key: Aid, investment and policies in Africa. Journal

of African Economies 8, 546-77

21 g Dowling, J.M., Hiemenz, U., 1983. Aid, savings, and growth in the Asian region. The Developing

Economies 21, 4-13

22 gc Durbarry, R., Gemmell, N., Greenaway, D., 1998. New evidence on the impact of foreign aid on

economic growth. Credit WP Univ. of Nottingham

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25 g Economides, G., Kalyvitis, S., Philippopoulos, A., 2004. Does foreign aid distort incentives and hurt

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and Business

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(LDCs): Further evidence. Studies in Comparative International Development Fall, 37-50

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World Bank Economic Review 12, 29-58

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Rica. Journal of International Development 12, 429-41

29 i Franco-Rodriguez, S., Morrissey, O., McGillivray, M., 1998. Aid and the public sector in Pakistan:

Evidence with endogenous aid. World Development 26, 1241-50

30 sp Fry, M.J., 1978. Money and capital or financial deepening in economic development? Journal of

Money, Credit, and Banking 10, 464-75

31 i Gang, I.N., Khan, H.A., 1991. Foreign aid, taxes and public investment. Journal of Development

Economics 34, 355-69

32 g Giles, J.A., 1994. Another look at the evidence on foreign aid led economic growth. Applied

Economics Letters 1, 194-99

33 sp Giovannini, A., 1983. The interest elasticity of savings in developing countries: The existing

evidence. World Development 11, 601-07

34 igc Gomanee, K., Girma, S., Morrissey, O., 2002. Aid and growth: Accounting for the transmission

mechanisms in Sub-Sahara Africa. Credit WP Univ. of Nottingham

35 g Gounder, R., 2001. Aid-growth nexus: Empirical evidence from Fiji. Applied Economics 33, 1009-19

36 sp Griffin, K.B., 1970. Foreign capital, domestic savings and economic development. Bulletin of the

Oxford University Institute of Economics and Statistics 32, 99-112

37 spg Griffin, K.B., Enos, J.L., 1970. Foreign assistance: Objectives and consequences. Economic

Development and Cultural Change 18, 313-27

38 gc Guillaumont, P., Chauvet, L., 2001. Aid and performance: A reassessment. Journal of Development

Studies 37, 66-92

39 g Gulati U.C., 1976. Foreign aid, savings and growth: Some further evidence. Indian Economic Journal

27

24, 152-60

40 g Gulati U.C., 1978. Effects of capital imports on savings and growth in less developed countries.

Economic Inquiry 16, 563-69

41 sp Gupta, K.L., 1970. Foreign capital and domestic savings: A test of Haavelmo’s hypothesis with cross-

country data: A comment. Review of Economics and Statistics 52, 214-16

42 sg Gupta, K.L., 1975. Foreign capital inflows, dependency burden, and saving rates in developing

countries: A simultaneous equation model. Kyklos 28, 358-74

43 sg Gupta, K.L., Islam, M.A., 1983. Foreign Capital, Savings and Growth – an International Cross-

Section Study. Dordrecht, Reidel Publishing Company

44 sig Gyimah-Brempong, K., 1992. Aid and economic growth in LDCs: Evidence from Sub-Saharan

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45 sigc Hadjimichael, M.T., Ghura, D., Mühleisen, M., Nord, R., Ucer, E.M., 1995. Sub-Saharan Africa:

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47 gc Hansen, H., Tarp, F., 2000. Aid effectiveness disputed. Journal of International Development 12,

375-398. Also pp 103-128 in Tarp, F., Hjertholm, P., eds. 2000. Foreign aid and develop-

ment. Lessons learnt and directions for the future. Routledge Studies in Development Econo-

mics: London

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70

49 i Heller, P.S., 1975. A model of public fiscal behavior in developing countries: Aid, investment, and

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World Development 20, 1481-88

55 i Khilji, N.M., Zampelli, E.M., 1994. The fungibility of U.S. military and non-military assistance and

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28

58 g Landau, D., 1990. Public choice and economic aid. Economic Development and Cultural Change 38,

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59 sig Larson, J.-D., 2001. An updated analysis of Weisskopf’s savings-dependency theory. Review of

Development Economics 5, 157-67

60 sg Lensink, R., 1993. Recipient government behavior and the effectiveness of development aid. De

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61 ig Lensink, R., Morrissey, O., 2000. Aid instability as a measure of uncertainty and the positive impact

of aid on growth. Journal of Development Studies 36, 30-48

62 gc Lensink, R., White, H., 2001. Are there negative returns to aid? Journal of Development Studies 37,

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63 i Levy, V., 1987. Does concessionary aid lead to higher investment rates in low-income countries?

Review of Economics and Statistics 69, 152-56

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65 gc Lu, S., Ram, R., 2001. Foreign Aid, government policies, and economic growth: Further evidence

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68 g Mbaku, J.M., 1993. Foreign aid and economic growth in Cameroon. Applied Economics 25, 1309-14

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74 ig Mosley, P., Hudson, J., Horrell, S., 1987. Aid, the public sector and the market in less developed

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30

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